Industrial mathematics : a course in solving real-world problems / Avner Friedman & Walter Littman.
Editor: Philadelphia : Society for Industrial and Applied Mathematics, 1994Descripción: xiii, 136 p. : il. ; 26 cmISBN: 0898713242Otra clasificación: 00A71 (00A06 00A69)CHAPTER 1. Crystal Precipitation [1] 1.1 The road ahead—Some helpful hints to the student [1] 1.2 Background [2] 1.3 The model [5] 1.4 Some facts about differential equations (BASIC) [7] 1.5 Picard’s method of successive approximations (BASIC) [10] 1.6 Nonrectangular regions (BASIC) [11] 1.7 The Euler method (or method of polygons) (BASIC) [12] 1.8 Crystals of single size 1.9 Remarks on Theorems 1.8.3-1.8.5 [16] 1.10 Reminder on Newton’s method [16] 1.11 The Runge-Kutta method (BASIC) [18] 1.12 Discussion and motivation (BASIC) [20] 1.13 Crystals of several sizes [22] 1.14 Summary [25] CHAPTER 2. Air Quality Modeling [27] 2.1 Background [27] 2.2 The model [29] 2.3 The advection equation [30] 2.4 Numerical methods [32] 2.5 The general advection equation [36] 2.6 Enters diffusion [36] 2.7 The von Neumann stability criterion [37] 2.8 Stability, consistency, and convergence [40] 2.9 Summary [45] CHAPTER 3. Electron Beam Lithography [47] 3.1 Background [47] 3.2 The mathematical model [48] 3.3 The heat equation [50] 3.4 The proximity effect [53] 3.5 The use of Fourier series [54] 3.6 The inclusion of backward scattering [58] 3.7 Computational experiments [59] 3.8 Summability of Fourier series [59] 3.9 Summary [61] 3.10 Appendix: Proof of Féjer’s theorem [63] CHAPTER 4. Development of Color Film Negative [69] 4.1 The process [69] 4.2 The mathematical model [71] 4.3 The bulk reaction problem [73] 4.4 Analysis of the solution [74] 4.5 Late development of film [77] 4.6 Implicit methods for solving system (4.12)-(4.16) numerically [78] 4.7 Summary [83] 4.8 Appendix: Proof of the strong maximum principle [83] CHAPTER 5. How Does a Catalytic Converter Function? [87] 5.1 Background [87] 5.2 The model [88] 5.3 The control problem [90] 5.4 A simplified model [91] 5.5 The calculus of variations [92] 5.6 The Euler-Lagrange equation [03] 5.7 The simplified control problem [05] 5.8 Determining the optimal control [09] 5.9 Summary [102] CHAPTER 6. The Photocopy Machine [105] 6.1 Background [105] 6.2 The photocopy machine [105] 6.3 The electric image [107] 6.4 Modeling the electric image [108] 6.5 Solving Poisson’s equations numerically [111] 6.6 Transmission conditions [115] 6.7 Computing the electric image [117] 6.8 A simple method for solving (6.18), (6.17) [119] 6.9 Summary [122] CHAPTER 7. The Photocopy Machine (Continued) [123] 7.1 The visible image [123] 7.2 Impossibility of a precise image [128] 7.3 Summary [132] Index [135]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A71 F911 (Browse shelf) | Available | A-7932 |
Includes bibliographical references and index.
CHAPTER 1. Crystal Precipitation [1] --
1.1 The road ahead—Some helpful hints to the student [1] --
1.2 Background [2] --
1.3 The model [5] --
1.4 Some facts about differential equations (BASIC) [7] --
1.5 Picard’s method of successive approximations (BASIC) [10] --
1.6 Nonrectangular regions (BASIC) [11] --
1.7 The Euler method (or method of polygons) (BASIC) [12] --
1.8 Crystals of single size --
1.9 Remarks on Theorems 1.8.3-1.8.5 [16] --
1.10 Reminder on Newton’s method [16] --
1.11 The Runge-Kutta method (BASIC) [18] --
1.12 Discussion and motivation (BASIC) [20] --
1.13 Crystals of several sizes [22] --
1.14 Summary [25] --
CHAPTER 2. Air Quality Modeling [27] --
2.1 Background [27] --
2.2 The model [29] --
2.3 The advection equation [30] --
2.4 Numerical methods [32] --
2.5 The general advection equation [36] --
2.6 Enters diffusion [36] --
2.7 The von Neumann stability criterion [37] --
2.8 Stability, consistency, and convergence [40] --
2.9 Summary [45] --
CHAPTER 3. Electron Beam Lithography [47] --
3.1 Background [47] --
3.2 The mathematical model [48] --
3.3 The heat equation [50] --
3.4 The proximity effect [53] --
3.5 The use of Fourier series [54] --
3.6 The inclusion of backward scattering [58] --
3.7 Computational experiments [59] --
3.8 Summability of Fourier series [59] --
3.9 Summary [61] --
3.10 Appendix: Proof of Féjer’s theorem [63] --
CHAPTER 4. Development of Color Film Negative [69] --
4.1 The process [69] --
4.2 The mathematical model [71] --
4.3 The bulk reaction problem [73] --
4.4 Analysis of the solution [74] --
4.5 Late development of film [77] --
4.6 Implicit methods for solving system (4.12)-(4.16) numerically [78] --
4.7 Summary [83] --
4.8 Appendix: Proof of the strong maximum principle [83] --
CHAPTER 5. How Does a Catalytic Converter Function? [87] --
5.1 Background [87] --
5.2 The model [88] --
5.3 The control problem [90] --
5.4 A simplified model [91] --
5.5 The calculus of variations [92] --
5.6 The Euler-Lagrange equation [03] --
5.7 The simplified control problem [05] --
5.8 Determining the optimal control [09] --
5.9 Summary [102] --
CHAPTER 6. The Photocopy Machine [105] --
6.1 Background [105] --
6.2 The photocopy machine [105] --
6.3 The electric image [107] --
6.4 Modeling the electric image [108] --
6.5 Solving Poisson’s equations numerically [111] --
6.6 Transmission conditions [115] --
6.7 Computing the electric image [117] --
6.8 A simple method for solving (6.18), (6.17) [119] --
6.9 Summary [122] --
CHAPTER 7. The Photocopy Machine (Continued) [123] --
7.1 The visible image [123] --
7.2 Impossibility of a precise image [128] --
7.3 Summary [132] --
Index [135] --
MR, 95g:00016
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